## New features of scattering from a one-dimensional non-Hermitian (complex) potential

Zafar Ahmed

For complex one-dimensional potentials, we propose the asymmetry of both reflectivity and transmitivity under time-reversal: $$R(-k)\ne R(k) and T(-k) \ne T(k)$$, unless the potentials are real or PT-symmetric. For complex PT-symmetry scattering potentials, we propose that $$R_{left}(-k)=R_{right}(k)$$ and $$T(-k)=T(k)$$.So far the spectral singularities (SS) of a one-dimensional non-Hermitian scattering potential are witnessed/conjectured to be at most one. We present a new non-Hermitian parametrization of Scarf II potential to reveal its four new features. Firstly, it displays the just acclaimed (in)variances. Secondly, it can support two spectral singularities at two pre-assigned real energies ($$E_*=\alpha^2,\beta^2$$) either in $$T(k)$$ or in $$T(-k)$$, when $$\alpha\beta>0$$. Thirdly, when $$\alpha \beta <0$$ it possesses one SS in $$T(k)$$ and the other in $$T(-k)$$. Lastly, when the potential becomes PT-symmetric $$[(\alpha+\beta)=0]$$, we get $$T(k)=T(-k)$$, it possesses a unique SS at $$E=\alpha^2$$ in both $$T(-k)$$ and $$T(k)$$.

http://arxiv.org/abs/1110.4485
Quantum Physics (quant-ph); Mathematical Physics (math-ph)